A spatiotemporally-nonlocal strain gradient theory for interpenetrating transient polymer networks

Abstract

Interpenetrating transient polymer networks having molecular intermixing can provide excellent mechanical performance and damping properties. In this paper, a new physics-based nonlocal strain gradient theory is proposed within the framework of thermodynamics to capture the microstructure-dependent and history-dependent effects of the interpenetrating transient polymer networks. The proposed theory not only accounts for the spatially-dependent nonlocal strain and its gradient effect but also captures the temporally-dependent behavior of the transient networks with bond exchange reactions, thereby called the spatiotemporally-nonlocal strain gradient theory. The nonlocal effects become particularly prominent because interpenetrating polymers have multiple chain lengths from sub-nanometer length scales to macroscopic scales, and the strain gradient becomes significant since the partially interleaved phenomenon in the two or more network microstructures of polymers can cause the difference among strains in each individual network microstructure. The spatiotemporally-nonlocal stress and spatiotemporally-nonlocal hyperstress can be predicted based on the microscopic descriptions of the interpenetrating transient polymer network, i.e., the chain energetics, the chain-length distribution function, the stretch ratio, and the exchange bond rate. Two examples are used to illustrate the application of the spatiotemporally-nonlocal strain gradient theory. One is to construct the spatiotemporally-nonlocal constitutive relation of an interpenetrating eight-chain polymer network with bond exchange reaction, and the other is to apply the spatiotemporally non-local constitutive relation for studying the longitudinal wave propagation behavior of polymer rods. The spatiotemporally nonlocal strain gradient models can link microscopic descriptions of polymer network structures to mechanical properties, thereby facilitating the exploration of transformative and disruptive high-performance materials through artificial design.